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[pseudo merlin]

Ahh ok thank you

[cedar kiln]

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[lavish spade]

on the fence about what i should use here

was tempted to go down the route of coefficient of friction but then its says smooth therefore that isnt an option

[cedar kiln]

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@lavish spade Has your question been resolved?

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[acoustic pivot]

Your acceleration downwards is g

Your acceleration towards the center is u^2/a

@lavish spade

tan(30) = 1/sqrt(3)

tan = opposite / adjacent

This is how I got that triangle

This is using the centripetal force formula

centripetal acceleration is v^2/r

[cosmic steppe]

<@&268886789983436800> this Shard guy keeps on posting "y = mx + b" for no reason

[cedar kiln]

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[crimson sedge]

Hi can someone help me

Please

[crimson sedge]

#❓how-to-get-help

[cedar kiln]

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[wind heart]

is y = x - 1 a linear function?

[maiden lodge]

y = mx+n -> y = 1*x - 1

[maiden lodge]

yes.

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[remote agate]

Hi, have a dice probability problem.
Say 3 dice are rolled. Without looking at the result, we are told that 2 dice are the same value. With that information, what is the chance of all 3 dice rolled being 555?

[remote agate]

Right now, i see that the chance of getting 555 is 1/216

chance that no numbers are the same : 6x5x4 = 120/216

so the chance that there are 2 the same or 3, is 96/216

[mental trail]

I think You're going the wrong way

[remote agate]

why?

[mental trail]

First, how many ways do you have of rolling 3 dice knowing the first 2 are the same ?

It's like you never rolled the second die in the first place

Because whatever the first die is, the second die will also be the same

[remote agate]

its not the first 2. its at least 2. sorry

i mean, out of the 3, we are told at least 2 are the same value

[mental trail]

Ok

[remote agate]

doesnt mention which order

[mental trail]

Ok sorry

[mental trail]

Ok so this is good

[remote agate]

so my answer is atm 1/216 : 96/216

which is 1/96

it seems correct, but some confirmation/tips would be nice

[mental trail]

Yeah It's correct, It's the definition of conditional probability

If you note A:"output is 555" and B:"2 dice are the same",
P(A|B) = P(A and B)/P(B)

But A and B is the same as A

[remote agate]

yeah, thats what i thought

sice 555 would be part of those 96/216

ok cool, thanks

.close

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[delicate patio]

my teacher gave me this question in one of the recent tests

and this was my solution to the problem

he gave me zero because he said that you took the solution way too complex and the answer is wrong

[crimson sedge]

Why write math in 6th century poetry handwriting

[delicate patio]

he just didn't check anything because idk he was not able to understand the solution maybe

[delicate patio]

wdym 😭

[vagrant elbow]

I think we should go back to before Francois Vieta and write math in stories and diagrams

[delicate patio]

can someone please help check the answer. I wrote it again in the best possible handwriting I could

?

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[zealous grail]

Someone help me how to multiply this

[livid hound]

apply basic distributive property as many times as needed

[zealous grail]

How?

[livid hound]

do you know the distributive property

[zealous grail]

I forgot 🙂

[livid hound]

would you be able to expand something like
a(b-c)?

[zealous grail]

a(ab-ac) like that?

[livid hound]

no

[crimson sedge]

yes but the a is gone

[zealous grail]

Ow

(ab+ac) like this?

[crimson sedge]

[zealous grail]

;-;

[crimson sedge]

do you know how to expand something like (a+b)(c+d)?

[livid hound]

(ab+ac) like this?
no

a(b**-**c) is not ab + ac

[zealous grail]

Like this?

$$18x³-24x+15x+20x-12x+16$$

[wraith dagger]

Sic3

[zealous grail]

Like this?

[livid hound]

no

[zealous grail]

Breh

[crimson sedge]

when you multiply x it becomes x squared

[zealous grail]

Csn u teach me it's so confusing

[livid hound]

start slowly, one step at a time if you're new to this

first demonstrate that you can apply the distributive property in the most basic form
a(b-c) = ?

[zealous grail]

ab-ac

[livid hound]

yes

and then apply that to

$\underbrace{(6x^2-5x+4)}{a}(\underbrace{3x}{b}-\underbrace{4}_{c})$

[wraith dagger]

ℝamonov

[zealous grail]

Multiply it?

[livid hound]

(don't skip to the next step yet)
take things slow for now

apply
a(b-c) = ab-ac
and only that, do not go further than that and do any additional expansions

[zealous grail]

(6x²)(3x)=18x³?

[livid hound]

is a true equation but not what i want from you

i've even braced the expressions with a,b,c for you

[zealous grail]

If i multiply (x²)(x) it becomes x³?

[crimson sedge]

yes

[livid hound]

again x^2*x is indeed x^3
but not what i want from you

[zealous grail]

Oh ok

[livid hound]

apply
a(b-c) = ab-ac
and only that, do not go further than that and do any additional expansions

[crimson sedge]

follow what he is trying to tell you

he put an example above

[zealous grail]

Another question if (6x²)(4)

It stays at 24x²?

[crimson sedge]

yes

[zealous grail]

Ok

[livid hound]

6x^2*4 is indeed 24x^2
but again is true but not what i want from you

are you going to keep ignoring my simple request?

[crimson sedge]

[zealous grail]

I don't get your question

🙂

And im solving

[crimson sedge]

do you understand this?

[zealous grail]

Ye

[crimson sedge]

you do the same just like what you did with a(b-c)

[livid hound]

apply $a(b-c) = ab - ac$ and nothing else to
$$\underbrace{(6x^2-5x+4)}{a}(\underbrace{3x}{b}-\underbrace{4}_{c})$$
(do not expand out $ab$ or $ac$) \
and tell me what you have after doing that

[wraith dagger]

ℝamonov

[zealous grail]

Another question about the 4 multiply by 3x what sign do i use? + Or -

[livid hound]

stop trying to skip ahead on your own

because you're typing seemingly relevant products but i have no idea what context you're multiplying in

[zealous grail]

Wait okay

I multiply first the 6x² and 3x and i got 18x³

Then

[livid hound]

again

not i want from you

[zealous grail]

I multiply the 6x³ and 4 and i got 20x

Why?

[livid hound]

again
not i want from you

read the above

[crimson sedge]

@zealous grail try expanding this

[livid hound]

all i want you to do is do the same thing to your expression (only the first step) and absolutely nothing else

the same thing that you applied to get from
a(b-c) to ab - ac (and nothing else)
do NOT make any attempts to multiply out the ab or ac

[zealous grail]

I got 18x³-20x² by multiplying the 6x² and (3x-4)

[livid hound]

again not what i want from you

using an example with numbers

applying a(b-c) = ab - ac
and nothing else to
5(7-3) would result in 5 * 7 - 5 * 3

[crimson sedge]

dude you should understand what you are supposed to be doing first

you need to get the logic behind this

[livid hound]

note how no attempts were made to simplify the 5 * 7 to 35 or 5 * 3 to 15

that's where i want you to stop

and tell me what you have

to ensure that you have the basic idea down before continuing

[zealous grail]

(6x²)3x-(6x²)4

Like that?

[livid hound]

where's the rest of it

[zealous grail]

Ok wait

[livid hound]

i've even braced the expressions with a,b,c for you

there is an alternate way to set it up, though I do want you to try and follow what I'm describing

[zealous grail]

$$(6x²)3x-(6x²)4-(5x)3x-(5x)4+(4)3x-(4)4$$

[wraith dagger]

Sic3

[zealous grail]

Like that?

Am i missing something?

[livid hound]

no,

you're not listening to my instructions again

[zealous grail]

So it's wrong?

[livid hound]

and making mistakes on top of that

[zealous grail]

What is my mistakes?

[livid hound]

well for one

you're not listening to my instructions again

which led to some sign screw ups because you effectively attempted to skip steps

$$\underbrace{(6x^2-5x+4)}{a}(\underbrace{3x}{b}-\underbrace{4}_{c})$$
can you see how the expressions were braced with $a,b,c$

[zealous grail]

What steps am i wrong?

[wraith dagger]

ℝamonov

[zealous grail]

I don't get your instructions that's why it's confusing

[livid hound]

you may be overthinking

i'm heavily breaking the question down

these are not supposed to be trick questions

[zealous grail]

Ye i am overthinking rn

[livid hound]

in that image

can you see that (6x^2-5x+4) is braced and under that is a

[zealous grail]

Im learning this by myself that's why it's hard for me

[zealous grail]

Ye

[livid hound]

likewise 3x is b
and 4 is your c

[zealous grail]

Ye

[livid hound]

using those, write the expression for
ab
(and i must insist on repeating, DO NOT EXPAND THIS OUT)

[zealous grail]

Like this?

$(6x^2-5x+4)3x-(6x^2-5x+4)4$

[wraith dagger]

Sic3

[zealous grail]

Like this?

[livid hound]

yes

that's all i really wanted from you

[zealous grail]

Oh

[livid hound]

for the first step

nothing more

nothing less

just the simple and only one application of a(b-c) = ab-ac

[zealous grail]

What's the next step?

[livid hound]

now apply the distributive property again

and hopefully don't mess up any of your signs

[zealous grail]

$(18x³-15x²+12x) - (24x²-20x+16)$
Like this?

[wraith dagger]

Sic3

[zealous grail]

Or no bracket?

[livid hound]

its currently fine, some of those were essential here,
some were not but those didn't hurt

[zealous grail]

I guess it's wrong

What signs do i need to correct?

[livid hound]

its currently fine,

[zealous grail]

Oh

There's no errors?

[livid hound]

its currently fine,

[zealous grail]

What do i do next?

[livid hound]

distribute that - sign,

[zealous grail]

How?

[livid hound]

by applying the distributive property

note that -k = -1 * k

[zealous grail]

The middle sign?

[livid hound]

yeh

[zealous grail]

I distribute it every number?

[livid hound]

this is no different to what you were just doing moments ago

[zealous grail]

How do i distribute the middle sign?

[livid hound]

-k = -1 * k

[zealous grail]

Can u give me a number instead of variable

[livid hound]

if it helps,
$$ - (24x²-20x+16) = -\red{1} \cdot (24x²-20x+16)$$

[wraith dagger]

ℝamonov

[zealous grail]

Oh

How did one go there?

[livid hound]

basic property of multiplication

[zealous grail]

So i distribute the minus sign to the left side?

[livid hound]

we just don't normally write the 1 because its unnecessary

by applying the distributive property
this is no different to what you were just doing moments ago

if you could distribute the 3x to the (6x^2-5x+4)
and distribute the 4 to (6x^2 - 5x+4)
you should have next no issue distributing
-1 to (24x²-20x+16)

[zealous grail]

So i just simplify the numbers?

[livid hound]

read my text bomb

[zealous grail]

Can u give an example cause i dont get it

[livid hound]

-1(a + b) = ?

[zealous grail]

(-1)a+(-1)b

[livid hound]

yeh

[zealous grail]

Like that?

[livid hound]

do the same thing

if you could distribute the 3x to the (6x^2-5x+4)
and distribute the 4 to (6x^2 - 5x+4)
you should have next no issue distributing
-1 to (24x²-20x+16)

[zealous grail]

$(-1)24x²-(-1)20x+(-1)16$

[wraith dagger]

Sic3

[livid hound]

yeh

[zealous grail]

-24x²+20x+16?

This?

[livid hound]

no

[zealous grail]

Why?

[livid hound]

-1*16 isn't 16

[zealous grail]

-16

[livid hound]

yes

[zealous grail]

Hey

I have anoher question

Is this correct?

[livid hound]

no

[zealous grail]

What's missing?

Am i missing the x at the last number?

[livid hound]

its not what missing, you have a lot of extra stuff that shouldn't be there

[zealous grail]

What should i do?

[livid hound]

divide 39x by x properly

[zealous grail]

Oh

Its 39

With no x right?

[livid hound]

yes

[zealous grail]

It's still wrong?

[livid hound]

show updated work

oh

13 * 5 isn't -65

[zealous grail]

I just copy the sign from the above

[livid hound]

why...

[zealous grail]

I watch the youtube videos

[livid hound]

what crappy vid are you watching

[zealous grail]

I forgot the name tho

[livid hound]

maybe you're misinterpreting what they did

[zealous grail]

I think so

[livid hound]

the red is the product of the things circled in green

[zealous grail]

This is correct?

[gusty forum]

try again, what's -26-65?

[zealous grail]

-91

Bruh whats the truth

-65 or +65?

[gusty forum]

what operation are you doing

[zealous grail]

Polynomial division

[gusty forum]

between 13x^2-26x and 13x^2+65x

[zealous grail]

Subtracting

[gusty forum]

so what's (13x^2-26x)-(13x^2+65x)

[zealous grail]

91x?

[gusty forum]

expand the brackets and find out

[zealous grail]

So my answer is

2x²+13x+91-455?

[gusty forum]

that's not how you treat the remainder

[zealous grail]

How?

I will add the remainder to 91?

[gusty forum]

a simple example, 3/2 gives you 1 with a remainder of 1

but does 3/2=1+1=2? no, you put the remainder on the divisor as a fraction, so you get 3/2=1+1/2

now figure out what to do with your remainder in the polynomial division :p

[zealous grail]

2x²+13x-91+ 452/x+5

[gusty forum]

why did the remainder suddenly change sign :p

[zealous grail]

Wai

Bruuhhhhh

Like this?

Or this 2x²+13x-91+458/x+5

??

[gusty forum]

bruh, what's 3 - (-455)

it really shouldn't be hard

[zealous grail]

Oh i forgot to replace

The sign

Wait i rewrite it all

Why?

[gusty forum]

spam, block and ignore

unfortunately mods seem to be away .-.

[zealous grail]

Like this?

[gusty forum]

alright we've got the same problems again

what's the operation between -91x+3 and 91x+455

[zealous grail]

Subtraction

[gusty forum]

but -91x-91x is not 0 so you borked something

wait you have the right -91 up top

bruh

[zealous grail]

My brain is not braining

[gusty forum]

you're subtracting so the thing on the left should line up exactly

so you have -91x on the left you should be subtracting -91x on the left to make it zero

it sound stupid but it works

[zealous grail]

(-91x)-(-91x)?

[gusty forum]

yes, expanding brackets would give you 0

[zealous grail]

Oh

So whats next?

(3)-(-455)?

[gusty forum]

which is?

[zealous grail]

Wait

Forgot to replace the sign

Like this?

[gusty forum]

hey we got there

[zealous grail]

Its correct?

[gusty forum]

now it is

[zealous grail]

Ty

.close

[cedar kiln]

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[harsh tide]

How to factor a binomial?

[harsh tide]

Give me a sec

,tex 8x³ - 729

[wraith dagger]

Ireneo SoNTS

[foggy merlin]

,w cube root of 729

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ｈｅｒｅｌｓ#1420

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[vague niche]

Small question about this exercise. Is this function continous by definition (polynomial and sine) or do I need to prove that it is continous at point 0 and then do the proof of the function being differentiable?

[primal violet]

it is continuous , everywhere but 0

[south tundra]

You can start with proving that it's differentiable yeah

[vague niche]

And since we have the case that the function is 0 when x is 0, is the full function continuous or do I need to prove that the function is continuous at point 0?

[south tundra]

If it's discontinuous the derivative won't exist anyways

[vague niche]

Yup, so it won't be differentiable

.close

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[limpid jolt]

,tex Suppose $(x, y, z) \in \mathbb{Z}^3 $ is a solution of $x^2 + y^2 = z^2 $.
Show that of the three numbers x, y and z at least 1 is divisible by 3,
at least 1 is divisible by 4 and at least 1 is divisible by 5.

[wraith dagger]

Magnus

[limpid jolt]

I don't know how to do this problem. Should i make into a cases problem? If so, what am i supposed to do?

[cedar kiln]

@limpid jolt Has your question been resolved?

[limpid jolt]

<@&286206848099549185>

[mental trail]

Proof by contradiction should be enough

[sacred grail]

[mental trail]

Study the congruent classes of squares respectively mod 3, mod 4 and mod 5

[sacred grail]

someone literally posted this exact problem

a moment ago

[mental trail]

Where?

[sacred grail]

#help-18 message

[mental trail]

Dayum

[sacred grail]

y'all in the same class lmao

[mental trail]

Some people in the same cla-

[limpid jolt]

Yeah

That guy is in same class

am i supposed to do this?:

,tex case 1: $x^2 \equiv$ 0 mod 3: \newline
...
\newline
case 1: $x^2 \equiv$ 0 mod 4: \newline
...
\newline
case 2: $x^2 \equiv$ 0 mod 5: \newline

[sacred grail]

bot is dead

[limpid jolt]

bruh moment

what type of cases are there for this?

the same i have?

[sacred grail]

just try all of them

there arent that many

[limpid jolt]

ok so lets say there is a case where x^2 is congruent to 0 mod 3, then what?

am i supposed to get the y^2 and z^2?

or should i do cases for both x^2 and y^2

so like case 1: x^2 = 0 mod 3 and y^2 = 1 mod 3

[sacred grail]

like say x^2 = 0 mod 3 then y^2 = 0, 1, z^2 = 0, 1 mod 3 are solutions

if x^2 = 1 mod 3 then y^2 = 0, z^2 = 1 is a solution

no matter what you do theres gonna be one of them = 0 mod 3

[limpid jolt]

and when i did those two cases then i should carry on to mod 4 and then to mod 5?

and that should prove the statement?

[sacred grail]

well if you have all of them != 0 mod 3, 4, 5

the equation is false

like +-1 + +-1 != +-1

[limpid jolt]

ok, but what if x^2 = -1 mod 5 and y^2 = -1 mod 5? isn't z^2 then -2 mod 5 and the equation is false?

[sacred grail]

?

[limpid jolt]

maybe i don't know modular arithmetic that well

[sacred grail]

z^2 cant be -2 mod 5

[limpid jolt]

oh

.close

[cedar kiln]

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[quasi slate]

4 qt = _____ oz

[quasi slate]

Can anyone help me solve this?

I'm having a heart attack

My answer is 128

But google says a different story

Like how is it 160

Can anyone care to explain?

[dull oxide]

https://www.checkyourmath.com/convert/volume/us_quarts_imperial_quarts.php#:~:text=A US quart is a,quarts in an Imperial quart.

Check your units

[quasi slate]

Okay

But

How

did google

come up

with 160

Can someone please care to explain

<@&286206848099549185>

[latent bloom]

Are you using US quart or Imperial quart?

US quart = 32 US ounces

[latent bloom]

Imperial quart = 40 imperial ounces

[quasi slate]

qt to fl oz

[quasi slate]

yeah

Us quart

Im using the US metric system

[latent bloom]

Then you multiply the quarts by 32 to get us ounces

[quasi slate]

Why 32 bw?

[rain drift]

32 oz in a quart and 4 qts to a gallon

[quasi slate]

Alright I see

Thanks guys

[latent bloom]

[quasi slate]

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[crimson sedge]

Hello,

I have to write a paper where I am planning to discuss applications of multivariable Calculus in economics.

I'm not sure how to go about it.

Like should I pick 4-5 topics
Like profit maximisation, utility maximisation, cost minimization and tell how partial derivatives and lagrange would play a role?

But like should I use generalised example of each in terms of x and y and tell how I would end up solving constraint optimization using Calculus?

Can someone please guide me if possible?

[crimson sedge]

I have to do a project related to multi calc

[cosmic steppe]

Optimization of an oil drum

Anything with production will deal with LaGrange multipliers

[cedar kiln]

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[cedar kiln]

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[polar echo]

Can somebody help

Its the first one

Without y

[quartz frost]

try to write it in sum notation

$\sum$

[wraith dagger]

~Martin

[soft owl]

it's production not sum

[quartz frost]

ohhh

[soft owl]

$\prod$

[quartz frost]

yeah

my bad

[wraith dagger]

Mehdi_Moulati

[polar echo]

I will try the both

Thx either

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[light pine]

ii help plz

[light pine]

not sure what to do

not sure about the hint either

[quartz frost]

alright

let E be the identity matrix

for all matrices M we know
M * E = E * M = M

[light pine]

yes

[quartz frost]

M(d,e,f)M(a,b,c)=M(d,e,f)

a trivial solution to this would be this:

M*E=M

so we want M(a,b,c) to be the identity matrix

do you know how the identity matrix looks like?

[light pine]

100 first row 010 2nd row 001 3rd?

[quartz frost]

correct

so we are looking at this

on the left is our matrix

on the right the identity

for them to be equal, what can we say about a,b,c?

[light pine]

ye

[light pine]

a = 0, b = 0, c = 0

[quartz frost]

correct

that is the solution

maybe you should include that 0 is in R

[cedar kiln]

@light pine Has your question been resolved?

[light pine]

hows this

[quartz frost]

exchange a0,b0,c0 for 0

then try to calculate the matrix product

[light pine]

like this?

[quartz frost]

do you understand that this equation is true?

[light pine]

wdym

identity multipled by anything gives u the anything

[light pine]

is this not correct?

[quartz frost]

it is

so where is the problem then?

[light pine]

there is no probelm

im just asking u if this answer looks correct

the way ive written it

[quartz frost]

it does

[light pine]

im gonna try iii now

[cedar kiln]

@light pine Has your question been resolved?

[light pine]

is this correct for iii?

[light pine]

<@&286206848099549185> could someone check this plz

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[glad kestrel]

do you know what a cofunction is?

[crimson sedge]

yes

i know i need to convert to sine

i know how to get exact values

[weak lake]

cos(x) = sin(90-x)

so what?

[crimson sedge]

so confused sorry

[weak lake]

i mean 69420

cos(x) also equals sin(x+90)

i prefer sin(x+90) cause of you think of the graph visually, its sin shifted left by 90 degrees

[crimson sedge]

what do i do with the"x" in cos(3pi/4+x)

[weak lake]

for example

cos(u) = sin(u+90)

u = 3pi/4 + x

[crimson sedge]

okay so x is 90

[weak lake]

no x is just x

[crimson sedge]

which is pi/2

[weak lake]

cos(u) = sin(u+90) is the identity

u is just a different variable to avoid confusion

[crimson sedge]

okay

[weak lake]

if you plug in x for u it would be cos((3pi/4+x)) = sin((3pi/4+x) + 90)

i added paranthesis to show how u can be subbed

but 69420 your program probably wants you to use cos(x) = sin(90 - x) instead of sin(x + 90)

for example cos(u) = sin(90 - u)

where u = 3pi/4 + x

so plug in 3pi/4 x for u in the equation above

[crimson sedge]

okay thank yoi

[weak lake]

i mean hopefully the u concept isnt confusing

im just expressing u in terms of x*

[crimson sedge]

yes thank you so much i couldnt find anything online

correct answer is -sin(pi/4+x)

[cedar kiln]

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[crimson sedge]

What sort of formula would I need to use with the values given to find the P-Value?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185> Sorry to ping again but I'm still unsure about this 😭

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[spice fjord]

i think what you need to do is use a normal distribution of the sample mean, so X’ ~ N(354, 12.3^2/n) where n is the size of the sample, n = 107

then you find the probability P(X’<355.7) but that gives you a p value of 0.9…, it’s quite weird that the 355.7 value doesn’t align with the alternate hypothesis

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[marble ermine]

Hello, Dumb question but i would like to understand somethin(video ahead)

[marble ermine]

https://www.youtube.com/watch?v=FnJqaIESC2s

They say in the conclusion that the average height of f(x) on an interval is the average slope of its antiderivative F(x) on that interval

so what's the link between f(x) slope and the area?

Because it only gives the link between average height and antiderivative slope here

[cedar kiln]

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[crisp quartz]

what does this symbol mean? https://i.gyazo.com/9028f71e9af43ab5f361f434a7969ab9.png

[crisp quartz]

~<

[cedar kiln]

@crisp quartz Has your question been resolved?

[mental trail]

Maybe typo

[crimson delta]

do you have more context?

I've seen something similar used to mean "roughly smaller" which can be useful in some contexts

but this seems like analysis something which shouldn't use a symbol like that

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[finite badger]

Trying to prove the left equal right (its not an equation)

Cant figure it out

Well it is an equation but has nothing yo do with degrees,just playing with indentities

[mental trail]

Express sin²(alpha) in terms of alpha/2

You should get to the result pretty quickly

[finite badger]

Oh i just didnt open the sin alpha correctly all this time

Ty

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[crimson sedge]

How do I go about doing this proof by induction? I've shown the base case by using X1 works but im unsure what to do after that

[crimson sedge]

xn-xn-1 = x1

use it

[tropic oxide]

your goal is $7(4^n - 3^n) - 12(4^{n-1} - 3^{n-1}) \overset?= 4^{n+1} - 3^{n+1}$

[wraith dagger]

Ann

[crimson sedge]

thanks

ill try

i dont know what to do from here tbh

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[wary estuary]

Back again, how should I do this:

How many "words" (just sets of letters pretty much) can be made out of ALL those letters: GNRFITWTFGNTGN ?

[elfin hemlock]

figure out how many words of length 1, length 2,...

[wary estuary]

They all have to be of length 14

Just all the possible combinations of all those letters

Would be easy if they weren't any repetition, but my brains not sure how to think of it with repetitions

[quartz vale]

look up permutations with like objects

[wary estuary]

alright, so:

14! / (3! * 3! * 3! *2!)

?

alright thanks

have a good day good sir

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[elder slate]

How to do number 14

[elder slate]

And 15

<@&286206848099549185>

[wary estuary]

Not 100% sure, but you could see this like a graph

As in you have two points (2, 0.3333) and (4, 0.75)

[elder slate]

Bruh

Complicate

D

[wary estuary]

Maybe get the "speed" (not sure if thats the proper word in english)

the rate of change or whatever

[elder slate]

I dont know how

[wary estuary]

Do you know the formula y2-y1/x2-x1

[elder slate]

Bruh no

[wary estuary]

Alright so, again, not sure if that's what you're supposed to do, but that's what I'd do:

(2, 0.3333) = x1, y1
(4, 0.75) = x2, y2

Plug that in the formula to get the speed, the rate of change:

0.75 - 0.333333 / 4 - 2

= 0.2083
So, hourly, they climb up that many stairs (in terms of percentage of the total of stairs)

Then, 1 / 0.2083 = 4.8 hours but that doesn't seem to be a reasonable answer, so yeah, a confirmation of someone else would be nice here

[elder slate]

The answer says 12:24

[wary estuary]

oh I misunderstood the question + just realized it wasn't linear anyways

[elder slate]

Ok

[wary estuary]

one sec i actually completely misunderstood it woww lol

[elder slate]

Did you get

[cedar kiln]

@elder slate Has your question been resolved?

[summer mulch]

14. First let's see how fast they march. How can you find that? See how much they traveled from 2 o'clock to 4 (total 2 hours). They traveled from 1/3 (33% of the way) to 3/4 (75% of the way). Total is 3/4 - 1/3, by applying method of subtracting fractions we have (3*3-4*1) / (4*3) = 5/12. This is how much they marched in 2 hours (roughly 41.6%). The problem asks when they did start matching which is before they covered first 1/3rd that we are given. We are going to find how much they needed to travel for that 1/3rd of the path. Let's use proprtions (I'll convert 2 hours to 120 minutes). 120 minutes for 5/12th of the way = x minutes for 1/3rd of the way. In numbers, 120 : 5/12 = x : 1/3. Let's find x, 120*(1/3) = x*(5/12). 40=x*(5/12). 40*12=x*5. 480=x*5. Finally, x=480/5, x=96 min. We needed 96 minutes to get to first third of the path, and at that time it was 2pm, so subtract 96 minutes, or 1 hour and 36 minutes, that's 1pm - 36 minutes = 12:24.

[elder slate]

How do you make the equation

[summer mulch]

which equation ?

[elder slate]

The 1201/3 = x5/12

[summer mulch]

you cross multiply the previous one

this two dots : is basically division

[elder slate]

I dont get it

[summer mulch]

Like this

or you can just take it step by step

first multiply both sides by left denominator then by right denominator

[elder slate]

Which numbers did you cross multiply

[summer mulch]

If you write it with two dots : you multiply outer with outer and inner with inner

[elder slate]

So 120x5 and 120x12

[summer mulch]

No treat 5/12 as a whole

thats why its in brackets

you can multiply by entire (5/12)

[elder slate]

How does 120:5/12 become 120 *1/3

[summer mulch]

I'll dm u

one sec

[elder slate]

Ok

[cedar kiln]

@elder slate Has your question been resolved?

[summer mulch]

15. I don't know how to do this in ratios so I would convert this to fractions. We do this by having same the same numerator but using total sum as denominator. https://www.learntocalculate.com/convert-ratio-to-fractions/. So 1:4 orange to lemonade is 1/5 oranges and 4/5 lemonade. 500 ml makes that 100 ml orange and 400 ml lemonade. Same concept for 1:3, we have 1/4 oranges and 3/4 lemonade which is 250ml oranges and 750ml lemonade. When we mix it we have 100+250 oranges to 400+750 lemonade. That's 350:1150. Reducing by 50 we get 7:23 ratio.

[cedar kiln]

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[modern crescent]

Is this series div or conv ?

[modern crescent]

I got it conv by L.C.T

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@modern crescent Has your question been resolved?

[true widget]

Converges

1/1+1/3+1/7+1/15+1/24 …

The numbers you add get progressively smaller

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[floral vale]

how do i solve this? ik how to usually solve these problems but how do i find the equation of the line tangent to an equation if the equation has two variable that cant be easily isolated like in this question?

[livid hound]

implicit differentiation/chain rule

[floral vale]

ohh i remember that

[floral vale]

so this would be the derivative right?

[livid hound]

no

you'd also need product rule for the derivative of xy

[floral vale]

i thought that is product rule

bc 1y+1x

oh i multiplied them

if derivative of xy is x+y do i add the y' for chain rule to both or just 1

so does d/dx(xy)=x+yy' or xy' + yy'

[floral vale]

@livid hound

[livid hound]

the former

if derivative of xy is x+y
no

[floral vale]

why isnt it the latter?

[livid hound]

should be clear if you apply product rule properly

[floral vale]

oh is it product rule first then chain rule

[livid hound]

yeh

[floral vale]

oh ok thanks

[floral vale]

is the x+y part for product rule wrong or were u talking about something else?

ohh nvm i see what you mean now sorry

im trying to solve for m now so i plugged in x1, and ended up with 3yy' = -6 but how do i find y from here?

[livid hound]

you also have the y-coord of the point

which you can plug into your derivative equation

[floral vale]

ohh ok

i ended up with this but it doesnt match the answer choices, did i mess up somewhere

[livid hound]

oh wait

misread what you typed earlier

all the derivatives of xy you had were wrong

should've been
$$\dv{x} (xy) = x \dv{x}y + y \dv{x}x = xy' + y$$

[wraith dagger]

ℝamonov

[livid hound]

has the x and y swapped around

[floral vale]

why is the x multiplied by y' instead

ohh nvm

i see now

only the x is multiplied by derivative of y

ok i solved it, thank you sm @livid hound

.close

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[crimson sedge]

Is this correct?

[crimson sedge]

Lambda is 0?

[sleek condor]

yeah

[crimson sedge]

Damn

Thanks

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[robust drift]

i keep getting a negative value when finding standard deviation

[robust drift]

i'll post my equation in one sec

$root(832/7) - 9.72^2$

[wraith dagger]

NightHorn

[robust drift]

= -83.58

[red pumice]

you probably forgot brackets

$\left(\sqrt{\frac{832}{7}} - 9.72\right)^2$

oof

[robust drift]

my data set was -3,8,8,10,14,15,16 if that helps

also i need to take awat the mean, it was a posative number before squareing

[wraith dagger]

Gijs

[robust drift]

no its just squareing the mean sorry

%root(Σx^2/n) - x̄$

[red pumice]

$root(Σx^2/n) - x̄$

[wraith dagger]

Gijs
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[red pumice]

$\sqrt{\sum \frac{(x-\bar{x})^{2}}{n}}$

[wraith dagger]

Gijs

[red pumice]

this?

[robust drift]

thats not how i was told but i think it's the same equation

[red pumice]

this is not what you were told?

[robust drift]

as in, in a different form

[red pumice]

$\sqrt{\frac{1}{n}\sum(x-\bar{x})^{2}}$

[wraith dagger]

Gijs

[red pumice]

was this it?

[robust drift]

no, i gtg anyway, thanks though

.close

[cedar kiln]

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[crimson sedge]

Hello everyone, can anyone help me out with the red marked question, please

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[jade edge]

How would you graph this equation?

[glass oasis]

do you know how to graph $y=x$

[wraith dagger]

張嘉棋

[jade edge]

Yes

No

[glass oasis]

huh?

[jade edge]

Wait

[glass oasis]

it's literally the most simplest graph

[jade edge]

I know how to graph in general

But

[glass oasis]

so you know how to graph straight lines?

[jade edge]

Idk what this one means as there is no fraction

Ummm

Do you mean horizontal and vertical lines?

[glass oasis]

no no

yk the straight line equation?

[jade edge]

Slopes?

Yeah

[glass oasis]

$y=-x$ is a slope

[wraith dagger]

張嘉棋

[jade edge]

Yeah

But

[glass oasis]

?

[jade edge]

Idk y that showed up

[glass oasis]

what showed up?

[jade edge]

Oh did u not see the do not dumb here thingy

It just showed up by accident

Ok but im still confused how to graph it

[glass oasis]

I didn't

[jade edge]

Ah ok

[glass oasis]

let's take an example

y=x

[jade edge]

Yeah?

[glass oasis]

the gradient of y=x is what?

[jade edge]

Whats a gradient???

Sorry I just started this unit

Is it one idk ;-;

[glass oasis]

gradient is the change in x over change in y

[jade edge]

Ah

One?

[glass oasis]

yup

and the y-intercept?

[jade edge]

Over 1?

[glass oasis]

???

[jade edge]

I rly dont know sorry

[glass oasis]

what don't you understand?

i'll try my best to explain

[jade edge]

Is the difference in the y intercept 0?

[glass oasis]

the y-intercept is where the line hits the y-axis

[jade edge]

Yeah

[glass oasis]

hence the appropriate name of y-intercept

so y=x

what is the y-intercept?

where does y=x hit the y-axis?

[jade edge]

Im not quite sure

[glass oasis]

so do you know the formula for a slope?

[jade edge]

Yes

[glass oasis]

recite it here pls

[jade edge]

Y= change in y over change in x plus the dependent variable at 0

[glass oasis]

so...?

$y=mx+c$

[wraith dagger]

張嘉棋

[jade edge]

Yeah

But how do you graph a slope of -1???

[glass oasis]

work backwards

from what you already know

it's easy to see

[jade edge]

Ughhh im sorry but I just don’t quite understand and If I do try I get a diagonal line

[glass oasis]

show me the graph of y=x

[jade edge]

Ok ok but question

One as a fraction is 1/1 right?

[glass oasis]

yes

1 as a fraction can also be 5/5 or 80/80 or 24/24 or it could be letters like x/x or apples/apples

[jade edge]

Is it not?

[glass oasis]

yuup thats the graph for y=x

[jade edge]

I was using the graph not the equation btw

[glass oasis]

yh ik

dw

[jade edge]

So is it the opposite with negative

Downward slope?

[glass oasis]

yup

you got it

[jade edge]

Oh!

[glass oasis]

show me first

cos idk how you think it is

[glass oasis]

perfect

👍

[jade edge]

Oh ok thank you

[glass oasis]

.close

do .close

[jade edge]

.close

[cedar kiln]

Channel closed

Closed by @jade edge

Use .reopen if this was a mistake.

[cedar kiln]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[keen merlin]

i dont understnad why this is 0.001 for the answer

I would appreciate if someone could help#

[gaunt hamlet]

Show your work

[dire geode]

Do ^

[keen merlin]

i did 0.1x0.1 = 0.01

[keen merlin]

It doesnt make sense how the answer would be 0.001

[gaunt hamlet]

Do you know Bayes theorem?

[keen merlin]

not too familiar with it

[gaunt hamlet]

Well, it says that P(A, given B) = P(B, given A)P(A)/P(B)

You want the probability that there's no detection, given that there's a storm

[keen merlin]

A and B are the events?

[gaunt hamlet]

Yes

[keen merlin]

so what would be events here

0.1

for the storm present

[gaunt hamlet]

A is there being no detection, B is there's a storm present

[keen merlin]

what would the value of a be?

*A

[gaunt hamlet]

P(A)? That's the probability that no storm was detected

[keen merlin]

I mean the value with reference to the question

[gaunt hamlet]

Well, what's the odds no storm is detected if there's a storm?

[keen merlin]

0.1?

[gaunt hamlet]

Yep

What's the odds there's a storm?

[keen merlin]

0.1

[gaunt hamlet]

So what's the odds no storm is detected if there's a storm AND there's a storm?

[keen merlin]

0.1 x 0.1

[gaunt hamlet]

Which is?

[keen merlin]

0.01

[gaunt hamlet]

Now let's do the opposite. What's the odds no storm is detected if there's no storm?

[keen merlin]

0.9

[gaunt hamlet]

You sure?

[keen merlin]

wait

wouldnt it be 100 percent

[gaunt hamlet]

Nope

[keen merlin]

ohh 0.05

no storm and its not detected

[gaunt hamlet]

No, that's the odds it is detected when there's no storm

What's the odds it is not detected

[keen merlin]

0.1 x 0.05

[gaunt hamlet]

No

The odds a storm is detected is 0.05

What's the odds it is not

[keen merlin]

0.95?

[gaunt hamlet]

Yes

And whats the odds there is no storm?

[keen merlin]

wait this is in the conditions there is no storm

[gaunt hamlet]

Yes

[keen merlin]

0.9

odds of no storm right?

[gaunt hamlet]

Yep

So the odds of no storm being detected AND there's no storm?

[keen merlin]

0.95 x 0.9

[gaunt hamlet]

Which is?

[keen merlin]

0.855

or 0.86

[gaunt hamlet]

Keep it exact. So what's the combined probability?

[keen merlin]

0.855

[gaunt hamlet]

Don't forget the other probability

From when there was a storm

[keen merlin]

Sorry what are you asking here?

[gaunt hamlet]

The odds of there being no detection and there's a storm is 0.01

The odds of there being no detection and there's no storm is 0.855

So what's the odds of there being no detection at all?

What's the combined probability?

[keen merlin]

0.01 x 0.855?

[gaunt hamlet]

No

Add them

Either there's a storm OR there isn't

[keen merlin]

0.865

[gaunt hamlet]

Yes

That's P(A)

The odds there's no storm detection in general

[keen merlin]

ok its a little confusing but its making sense

[gaunt hamlet]

So what's P(B, given A)

The odds there's a storm, given there was no detection?

Wait wait wait

Misread the question

But the work was not for nothing

We wants the odds there was no detection AND there's a storm

So the probability we found was useful

[keen merlin]

yea thats fine, ive learnt something at least 🙂

[gaunt hamlet]

We know the odds there was no detection

What's the odds there's a storm

[keen merlin]

0.9?

[gaunt hamlet]

The odds there is a storm, sorry

[keen merlin]

ohh 0.1

[gaunt hamlet]

So the odds of there being no detection AND there's a storm?

Weird

Gimme a sec

[keen merlin]

no problem take your time

[gaunt hamlet]

Fuck

I think you were right to begin with

0.1 * 0.1

Goddammit

There must be a typo or something because as written, I think the answer is 0.01

[keen merlin]

i was wondering the route you took 😅

it should be 0.01 right?

[gaunt hamlet]

All cuz I misread the problem -_-

Worst part? The way I read it, the answer is given in the question

No work necessary

Fml

[keen merlin]

yea i think you are too advanced for question like this 🤣

[gaunt hamlet]

It's 10pm I'm too tired for this shit

Anyways yeah its 0.01

[keen merlin]

yea tbh he aint the most english literate

his questions are a bit confusing